Vinicius Jr scored in Real Madrid's 4-1 at Levante.
The Brazil international, however, also left Elgezabal furious after he physically confronted him as Kylian Mbappe was about to take his successful 64th minute penalty.
Afterwards, Elgezabal said: "I don't want to fuel the controversy further. It's true that when we show disrespect, not just to ourselves but also to the fans, we have to say enough.
"He's a player with enormous potential, but there are situations that affect us personally. I think it was inappropriate , and I don't want to give him more importance than he deserves, because it's unnecessary."
The Levante captain then commented on the result: "We're not satisfied, because no one likes to lose. We knew it would be a difficult match, but we really wanted to compete, regardless of the opponent, and we wanted to prove ourselves at home. Now we have to turn the page, try to improve and clear our minds."